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Linear Regression Clash Story
- A researcher used linear regression with a binary outcome, insisting it was valid despite misfit concerns.
- This led to frustration and hostility over logistic regression necessity, highlighting misunderstandings in statistical modeling.
Limitations of Linear Models for Binary
- Linear models fail for binary outcomes because predicted probabilities can fall outside 0 and 1 boundaries.
- Residuals violate assumptions, making logistic regression more suitable for binary data modeling.
S-curve in Binary Outcomes
- Binary outcomes are inherently non-linear, leading to an S-shaped probability curve rather than a linear response.
- Logistic regression captures this natural S-curve to model probabilities between zero and one.